Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13070844 | C2 | semidirect |
| 4. #13066688 | C2 | semidirect |
| 5. #13066673 | C2 | semidirect |
| 6. #13066666 | C2 | semidirect |
| 172. C11 | #12469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070844 | 2 |
| #13068015 | 2 |
| #13067981 | 2 |
| #13066688 | 2 |
| #13066673 | 2 |
| #13066666 | 2 |
| D4×C11×C16 | 2 |
| #12469 | 11 |